Communications in Mathematical Sciences

Volume 19 (2021)

Number 2

Scattering for 3D quantum Zakharov system in $L^2$

Pages: 383 – 404



Chunyan Huang (School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China)

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Yi Heng (School of Computer Science and Engineering, Sun Yat-Sen University, Guangzhou, China)


In this paper, we study the Cauchy problem for quantum Zakharov system in three space dimensions. We prove that the quantum Zakharov system scatters in low regularity space $L^2$ with small radial initial data basing on some radial improved Strichartz estimates with wider range and the normal form transformation technique.


quantum Zakharov system, scattering, global well-posedness

2010 Mathematics Subject Classification

35L05, 35L30, 35Q55

Chunyan Huang is supported by the National Natural Science Foundation of China (No.11971503), the Young Talents Program (No. QYP1809) and the disciplinary funding of Central University of Finance and Economics. Yi Heng acknowledges support provided by the “Young overseas high-level talents introduction plan” funding of China and Zhujiang Talent Program of Guangdong Province (No. 2017GC010576).

Received 23 March 2020

Accepted 7 September 2020

Published 12 April 2021